UAMP-SBL works well with a simple single loop iteration, which is in contrast to the double loop iterative algorithm GGAMP-SBL [1]}. The complexity of UAMP-SBL black(with UAMPv2) is dominated by two matrix-vector product operations in Line 2 and Line 9, i.e., \(\mathcal {O} (MN)\)  per iteration. The algorithm typically converges fast and delivers outstanding performance as shown in blackSection VI. blackUAMP-SBL involves an SVD , but it only needs to be computed once and may be carried out off-line. The complexity of economic SVD is \(\mathcal {O} (\min \lbrace M^2N, MN^2\rbrace )\) . Note that for the runtime comparison in blackSection VI, we do not assume off-line SVD computation, and the time consumed by SVD is counted for UAMP-SBL.
